The ability to measure climatic changes in ocean temperature is fundamentally limited by the presence of mesoscale variability. Because ocean acoustic propagation can be used to measure the range‐averaged temperature profile, long‐range acoustic transmissions have been proposed as a means of filtering out mesoscale variability in order to measure a global warming related trend in mean temperature. In this paper, the Cramer–Rao lower bound (CRLB) on the estimation of the mean depth‐dependent temperature profile given a single acoustic transmission is evaluated to provide an indication of the highest accuracy which could be achieved by this experiment. The CRLB derived here applies to broadband vertical arrays of arbitrary length and thus extends previous work. Evaluation of the bound is performed using models of sound‐speed variability derived from real Pacific environmental data. Results indicate that the performance of an acoustic thermometry system is limited by mesoscale variability above a threshold value of observation–time–signal‐to‐noise ratio product and is acoustic noise limited below this threshold. Further, comparisons of the CRLB above this threshold suggest that for a 5000‐km source–receiver separation, ATOC accuracy may vary from between 0.01 and 0.1 °C depending on the shape and uncertainty of the change in mean temperature profile.